7. Note that the roots for characteristic equation of u" - 4u = 0 are 2, -2. Given the initial conditions u(0) = 5 and u'(0) = 4, (a). Find the solution to the IVP using the exponential form of the general solution: u(t) = C₁e²t + C₂e-2t (b). Find the solution to the same IVP using the hyperbolic form of the general solution: u(t) = C₁ cosh 2t + C₂ sinh 2t
7. Note that the roots for characteristic equation of u" - 4u = 0 are 2, -2. Given the initial conditions u(0) = 5 and u'(0) = 4, (a). Find the solution to the IVP using the exponential form of the general solution: u(t) = C₁e²t + C₂e-2t (b). Find the solution to the same IVP using the hyperbolic form of the general solution: u(t) = C₁ cosh 2t + C₂ sinh 2t
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:7. Note that the roots for characteristic equation of u" - 4u = 0 are 2, -2.
Given the initial conditions u(0) = 5 and u' (0) = 4,
(a). Find the solution to the IVP using the exponential form of the general solution: u(t) = C₁e²t + C₂e-²t
(b). Find the solution to the same IVP using the hyperbolic form of the general solution: u(t) = C₁ cosh 2t + C₂ sinh 2t
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